Disruptive events lead to capacity degradation of transportation infrastructure, and a good restoration plan could minimize the aftermath impacts during the recovery period. This is considered one aspect of resiliency for transportation systems. Although unmet demand has been proposed as one measure of resilience for freight transportation, it has rarely been used for general transportation systems. This study takes unmet demand and total travel time as two measures in modeling the restoration plan problem and proposes a bi-objective bi-level optimization framework to determine an optimal transportation infrastructure restoration plan. The lower-level problem uses Elastic User Equilibrium to model the imbalance between demand and supply and measures the unmet demand for a given transportation network. The upper-level problem, formulated as bi-objective mathematical programming, determines optimal resource allocation for roadway restoration. The bi-level problems are solved by a modified active set algorithm and a network representation method derived from Network Design Problems. The Weighted Sum Method is adopted to solve the Pareto Frontier of this bi-objective optimization problem. The proposed restoration plan optimization method was applied to a typical road network in Sioux Falls, to verify the effectiveness of the methodology. For a given failure scenario, the Pareto Frontier of this bi-objective bi-level optimization problem with various budget levels, cross-referring to the travel efficiency of each solution, was illustrated to demonstrate how the proposed method can support decision-making for road network restoration. To further study the performance of the proposed method, different scenarios were generated with one to five links disrupted and the proposed methodology was applied with different budget levels. The statistical analysis of the optimized solutions for these scenarios demonstrates that a higher budget could help reduce unmet demand in the system by providing more restoration options.

破坏性事件导致交通基础设施的能力下降，制定良好的恢复计划可以最大程度地减少恢复期间的善后影响。这被认为是运输系统的弹性的一方面。尽管未满足的需求已被提出作为货运抗灾能力的一种措施，但很少用于一般运输系统。这项研究将需求未满足和总旅行时间作为建模恢复计划问题的两个措施，并提出了一个双目标双层优化框架来确定最佳的交通基础设施恢复计划。较低层的问题使用弹性用户均衡来模拟需求和供应之间的不平衡，并测量给定交通网络的未满足需求。上层的问题 公式化为双目标数学规划，可确定道路修复的最佳资源分配。通过改进的活动集算法和源自网络设计问题的网络表示方法来解决双层问题。采用加权求和法求解该双目标优化问题的帕累托边界。拟议的修复计划优化方法被应用于苏福尔斯市的典型道路网络，以验证该方法的有效性。对于给定的故障场景，说明了具有不同预算水平的这种双目标双级优化问题的帕累托边界，并交叉引用了每个解决方案的旅行效率，以说明所提出的方法如何支持道路决策。网络恢复。为了进一步研究所提出的方法的性能，生成了具有一到五个链接中断的不同方案，并在不同的预算水平上应用了所提出的方法。针对这些方案的优化解决方案的统计分析表明，更高的预算可以通过提供更多还原选项来帮助减少系统中未满足的需求。